For each of the following linear operators T on a vector space V, test T for...

 

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For each of the following linear operators T on a vector space V, test T for diagonalizability, and if T is diagonalizable, find a basis for V such that [T] is a diagonal matrix. (a) VP3(R) and T is defined by T(f(x)) = f'(x) + f"(x), respec- tively. (b) VP2(R) and T is defined by T(ax + bx + c) = cx + bx+a. For each of the following linear operators T on a vector space V, test T for diagonalizability, and if T is diagonalizable, find a basis for V such that [T] is a diagonal matrix. (a) VP3(R) and T is defined by T(f(x)) = f'(x) + f"(x), respec- tively. (b) VP2(R) and T is defined by T(ax + bx + c) = cx + bx+a.

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a Given V P3R the vector space of polynomials of degree at most 3 with real coefficients and the lin... View the full answer